The BRRip is a compressed version of an already ripped Blu-Ray disk. It's virtually a 1080p mkv file that is then ripped again to make it smaller in size (same size as a DVD). The BDRip comes straight from the Blu-Ray disk and should essentially have better quality. The main reason why BDRips are better is because if the source used for BRRip's has problems, so will the BRRip.

BDRip / BRRip vs DVD5 / DVD9
The standard retail DVD uses a resolution of 720Ã—480 (NTSC) or 720Ã—576 (PAL), but you will see that Blu-Ray rips (in these XviD *.avi files, and otherwise) offer better video quality than DVD5 or DVD9 disks, even on an HDTV. This is because the source for BRRips and BDRips (obviously being a Blu-Ray disk), is in full 1080p resolution. When done correctly by employing the proper filtering techniques, much of the HQ detail can be retained even in a smaller resolution.

Below is a comparison of screenshots from D-ZON3’s BRRip and DEViSE’s DVDRip (x264):

As you can see from the two screenshots above, the BRRip is clearly far more detailed compared to the DVDRip.